Semiclassical asymmetric top in action–angle variables with binary stereodynamics

Abstract

A model is examined for the levels of an asymmetric, rigid top based on action-angle variables and including two basis forms for its rotational stereodynamics, in each of which the analytic expression for the axial action is quantized and does not require matrix diagonalization, is more transparent, and can be used for rapid computations. The maximum (on the order of the rotational constant) deviations of the model energies of the levels from their exact values occur in the separatrix between the basis forms and fall off by orders of magnitude with increasing distance from it. The model shows that the absolute magnitude of the anisotropy in the time averaged cross section of the dipole transition for tops with arbitrary orientation of the transition dipole moment differs greatly in the stereodynamic basis forms. In each of these the anisotropy depends more strongly on the pseudoquantum numbers than on the principal quantum number, and falls off as the latter decreases.